SINGAPORE, May 14 (Reuters) - Iron ore futures in China fell for a fifth day in six on Wednesday, pressured by lean buying interest in the world's top consumer of the raw material amid slow demand for steel.

A potential workers' strike at Australia's Port Hedland, which could halt a fourth of global iron ore shipments, has not deterred bearish investors from bidding down prices, arguing a shortage in supply may take weeks to be felt given towering stockpiles at ports in China.

Australian miner Fortescue Metals Group is offering a bigger discount for its lower grade iron ore cargoes for shipment in June amid weaker demand, traders said.

Iron ore for September delivery on the Dalian Commodity Exchange, the most-traded contract, was down 0.7 percent at 738 yuan ($120) a tonne by midday.

"The physical market for steel is not that good and people are pessimistic because of what's happening in the real estate market. They are very reluctant to buy," said an iron ore trader in China's eastern Shandong province.

The most-active rebar for October delivery on the Shanghai Futures Exchange dropped 0.4 percent to 3,168 yuan a tonne.

Rebar fell to 3,152 yuan on Monday, the second lowest for a most-traded contract since the Shanghai bourse launched them in 2009.

The decline in Chinese iron ore futures came as market participants shrugged off a looming strike by tugboat workers in Port Hedland.

While a full blown strike could halt exports from the port which is operating at near capacity of 1 million tonnes a day, a "supply shortage would take several weeks to work through the system, given China's port stocks remain above 100 million tonnes last week," Australia and New Zealand Banking Group said in a note.

"Anecdotal market feedback suggests supply disruptions from potential strike action in the Pilbara won't be a major factor and any price rally short-lived," ANZ said.

Global supply is expected to be brisk this year as top iron ore producers such as Rio Tinto are forging ahead with plans to boost output, confident their low-cost operating model would allow them to prevail over smaller, higher-cost suppliers to China.

Rio Tinto, the world's No.2 iron ore miner, said it had increased its annual production capacity to 290 million tonnes two months ahead of schedule and is on course to lift it further to 360 million tonnes by 2017.

FORTESCUE DISCOUNT

But some iron ore traders are looking at taking advantage of weaker iron ore prices.

"We are planning to buy iron ore because we believe that the current index price is very near the bottom although it is possible that it could hit $90 or $95," the Shandong-based trader said.

"We only have 100,000 tonnes of ready stock at the ports so we might purchase another 250,000 tonnes. We believe the cost now is low and the risk is limited."

The trading firm is looking at buying a cargo from Fortescue which is offering an 8.5 percent discount to the Platts 62-percent iron ore index price for June cargoes for its lower grade material with iron content of 56 to 57 percent, he said.

That was a deeper discount to the 7.5 percent that Fortescue offered for May cargoes and the 6.5 percent cut in April, the trader said.

"They give very attractive discounts. I don't think the other big miners are doing that," he said.

Iron ore for immediate delivery to China .IO62-CNI=SI last stood at $103 a tonne on Monday, not too far above a near 20-month low of $102.70 reached the prior trading day. The price has fallen more than 23 percent this year.

Data compiler Steel Index did not publish a spot price index on Tuesday because it was a public holiday in Singapore. Publication of the index resumes on Wednesday.